Heterotic phase transitions and singularities of the gauge dyonic string

TL;DR

This paper explores phase transitions and singularities in heterotic strings on K3, revealing conditions under which dyonic string solutions become tensionless or singular, and highlighting special self-dual cases with regular solutions.

Contribution

It generalizes heterotic dyonic string solutions to include gauge instantons and analyzes their behavior at phase transitions, identifying conditions for tensionless and regular solutions.

Findings

Vacua with phase transitions have naked singularities in string solutions.

Self-dual gauge configurations lead to regular, non-singular solutions.

Certain instanton configurations result in tensionless strings at critical couplings.

Abstract

Heterotic strings on $R^6 \times K3$ generically appear to undergo some interesting new phase transition at that value of the string coupling for which the one of the six-dimensional gauge field kinetic energies changes sign. An exception is the $E_8 \times E_8$ string with equal instanton numbers in the two $E_8$'s, which admits a heterotic/heterotic self-duality. In this paper, we generalize the dyonic string solution of the six-dimensional heterotic string to include non-trivial gauge field configurations corresponding to self-dual Yang-Mills instantons in the four transverse dimensions. We find that vacua which undergo a phase transition always admit a string solution exhibiting a naked singularity, whereas for vacua admitting a self-duality the solution is always regular. When there is a phase transition, there exists a choice of instanton numbers for which the dyonic string is tensionless and quasi-anti-self-dual at that critical value of the coupling. For an infinite subset of the other choices of instanton number, the string will also be tensionless, but all at larger values of the coupling.